10001111000110

10001111000110 is a binary number. In the decimal system, this number translates to 15574. Binary is a base-2 numeral system, meaning it uses only two symbols: 0 and 1. Each digit in a binary number represents a power of 2. Reading from right to left, the digits in 10001111000110 correspond to the following powers of 2: 2^0, 2^1, 2^2, 2^3, and so on. Therefore, to convert 10001111000110 to decimal, we multiply each binary digit by its corresponding power of 2 and sum the results. In this case, the calculation would be (1 * 2^13) + (0 * 2^12) + (0 * 2^11) + (0 * 2^10) + (1 * 2^9) + (1 * 2^8) + (1 * 2^7) + (1 * 2^6) + (0 * 2^5) + (0 * 2^4) + (0 * 2^3) + (1 * 2^2) + (1 * 2^1) + (0 * 2^0). This summation equals 8192 + 0 + 0 + 0 + 512 + 256 + 128 + 64 + 0 + 0 + 0 + 4 + 2 + 0, which equals 9158. However, a re-evaluation of the binary string reveals a different decimal equivalent. The correct calculation for 10001111000110 is (1 * 2^13) + (0 * 2^12) + (0 * 2^11) + (0 * 2^10) + (1 * 2^9) + (1 * 2^8) + (1 * 2^7) + (1 * 2^6) + (0 * 2^5) + (0 * 2^4) + (0 * 2^3) + (1 * 2^2) + (1 * 2^1) + (0 * 2^0) = 8192 + 0 + 0 + 0 + 512 + 256 + 128 + 64 + 0 + 0 + 0 + 4 + 2 + 0 = 9158. Upon further review, the provided binary string is 10001111000110. Its decimal conversion is (1 * 2^13) + (0 * 2^12) + (0 * 2^11) + (0 * 2^10) + (1 * 2^9) + (1 * 2^8) + (1 * 2^7) + (1 * 2^6) + (0 * 2^5) + (0 * 2^4) + (0 * 2^3) + (1 * 2^2) + (1 * 2^1) + (0 * 2^0) = 8192 + 0 + 0 + 0 + 512 + 256 + 128 + 64 + 0 + 0 + 0 + 4 + 2 + 0 = 9158. Correction: The binary number 10001111000110 is equivalent to the decimal number 9158. The initial interpretation of the decimal value was incorrect. Binary numbers are fundamental in computer science and digital electronics, forming the basis of all digital data representation.